For the two dimensional Toda equations corresponding to the Kac-Moody algebras C_l⁽¹⁾ and D_l+1⁽²⁾, the Darboux transformations which keep all the reductions of the Lax pairs are constructed. The lowest degrees of the Darboux transformations are 2l+2 for C_l⁽¹⁾ and 2l for D_l+1⁽²⁾. Exact solutions of these Toda equations are presented in a purely algebraic way.

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